Anisotropic viscoelastic properties of cortical bone

Toshiya Iyo, Yasuyuki Maki, Naoki Sasaki, Mitsuo Nakata

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Abstract

Relaxation Young's modulus of cortical bone was investigated for two different directions with respect to the longitudinal axis of bone (bone axis, BA): the modulus parallel (P) and normal (N) to the BA. The relaxation modulus was analyzed by fitting to the empirical equation previously proposed for cortical bones, i.e., a linear combination of two Kohlraush-Williams-Watts (KWW) functions (Iyo et al., 2003. Biorheology, submitted):E(t)=E0{A 1 exp[-(t/τ1)β]+(1-A1) exp[-(t/τ2)γ]},[0<A1,β, γ<1],where E0 is the initial modulus value E(0). τ1 and τ2(≫τ1)are characteristic times of the relaxation, A1 is the fractional contribution of the fast relaxation (KWW1 process) to the whole relaxation process, and β and γ are parameters describing the shape of the relaxation modulus. In both P and N samples, the relaxation modulus was described well by the empirical equation. The KWW1 process of a P sample almost completely coincided with that of an N sample. In the slow process (KWW2 process), there was a difference between the relaxation modulus of a P sample and that of an N sample. The results indicate that the KWW1 process in the empirical equation represents the relaxation in the collagen matrix in bone and that the KWW2 process is related to a higher-order structure of bone that is responsible for the anisotropic mechanical properties of bone.

Original languageEnglish
Pages (from-to)1433-1437
Number of pages5
JournalJournal of Biomechanics
Volume37
Issue number9
DOIs
Publication statusPublished - Sep 2004
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Orthopedics and Sports Medicine

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